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Iota energy of weighted digraphs | ||
| Transactions on Combinatorics | ||
| مقاله 5، دوره 7، شماره 3، آذر 2018، صفحه 55-73 اصل مقاله (277.34 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2018.109248.1546 | ||
| نویسندگان | ||
| Sumaira Hafeez1؛ Mehtab Khan* 2 | ||
| 1School of Natural Sciences, National university of sciences and Technology Islamabad, Pakistan | ||
| 2Department of mathematics, school of Natural Sciences, National University of Sciences and Technology Islamabad, Pakistan | ||
| چکیده | ||
| The eigenvalues of a digraph are the eigenvalues of its adjacency matrix. The iota energy of a digraph is recently defined as the sum of absolute values of imaginary part of its eigenvalues. In this paper, we extend the concept of iota energy of digraphs to weighted digraphs. We compute the iota energy formulae for the positive and negative weight directed cycles. We also characterize the unicyclic weighted digraphs with cycle weight $ r \in [-1, 1]\backslash \{0\}$ having minimum and maximum iota energy. We obtain well known McClelland upper bound for the iota energy of weighted digraphs. Finally, we find the class of noncospectral equienergetic weighted digraphs. | ||
| کلیدواژه‌ها | ||
| Weighted digraphs؛ Extremal energy؛ Equienergetic weighted digraphs | ||
| مراجع | ||
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